Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the...
FURTHER MATHEMATICS
WAEC 2012
Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.
- A. \(5\sqrt{3} - 3\)
- B. \(3 - 5\sqrt{3}\)
- C. \(5 - 3\sqrt{3}\)
- D. \(3\sqrt{3} - 5\)
Correct Answer: A. \(5\sqrt{3} - 3\)
Explanation
\(F = F \cos \theta i + F \sin \theta j\)
\(10N = 10 \cos 60 i + 10 \sin 60 j\)
\(6N = -6 \cos 330 i - 6 \sin 330 j\)
\(R_{x} = 10 \cos 60 - 6 \cos 330 \)
= \(10 \times \frac{1}{2} - 6 \times \frac{\sqrt{3}}{2}\)
= \(5 - 3\sqrt{3}\)
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